The interaction of infrared-active molecular vibrations with quantized electromagnetic field modes of optical Fabry-Pérot-type cavities has been experimentally shown to have a peculiar impact on chemical ground state reactivity and molecular properties[1]}, [2]}, [3]}, [4]}, [5]}. The origin of this impact is attributed to the formation of vibrational light-matter hybrid states, known as vibrational polaritons[2]}. Linear[3]}, [4]}, [9]} and nonlinear[10]}, [11]} infrared spectroscopic techniques have been the experimental methods of choice to characterize these vibrational light-matter hybrid states. Consequently, there has been a decent amount of theoretical effort to address the calculation of infrared spectra for vibro-polaritonic systems[12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}. There, one or more molecular vibrations interact with a single or multiple quantized cavity modes and the composite system is commonly described by an effective vibrational Pauli-Fierz Hamiltonian in the length-gauge representation of non-relativistic cavity quantum electrodynamics (cQED)[19]}, [20]}, [21]}, [22]}. In the latter, the light-matter interaction is mediated by the molecular ground state dipole moment and its orientation relative to the cavity mode polarization directions. Often, the dipole moment is assumed to be either exactly aligned with the polarization direction of a cavity mode or fixed at a certain orientation with respect to a single cavity mode
polarization.
The impact of molecular rotations on vibrational polaritons, which naturally influences the light-matter coupling due to the orientation dependent nature of the interaction, has been addressed only recently in a few works[23]}, [24]}, [25]}. There, the orientation of the dipole moment was allowed to vary with respect to the polarization direction of a single cavity mode. However, the quantization of the cavity radiation field naturally leads to doubly degenerate optical modes with two orthogonal polarization directions[26]}, which both should be relevant for the light-matter interaction of rovibrating molecules.
